Eq. 9.0.1 for a broadband signal after delay compensation and
integration (time average) can be written as
A block diagram of an XF correlator is shown in Fig. 9.5. In this diagram, fractional delays are compensated for by changing the phase of the sampling clock. After delay compensation, the cross correlations for different delay are measured using delay lines and multipliers, which are followed by integrator. Since the cross correlation function in general is not an even function of , the delay compensation is done such that the correlation function is measured for both positive and negative values of in the correlator. The zero lag autocorrelations of the signals are also measured, which is used to normalize the cross correlation. The quantization correction (block marked as F) is then applied to the normalized cross correlations. The cross spectrum is obtained by performing a DFT on the corrected cross correlation function. A peculiarity of this implementation is that the correlations are measured first and the Fourier Transform is taken later to get the spectral information. Hence it is called an XF correlator.